The SMC X-1 scan shape test changes with time weights and orbital cuts in 2012–2023

We test whether the mean long-cycle curves of SMC X-1 are proportional in the MAXI 2–4 and 4–10 keV bands. We use 12,954 individual scans in 64 selected Swift/BAT cycles from 2012 through 2023. Each scan stays within binary orbital phase 0.15–0.45. The main fit uses three cycle harmonics, additive year and orbital terms, and the same time weights in both bands. A common linear projection preserves any noiseless proportional signal, even if the curve model omits part of its shape. The main loss increase is 11.3644. Paired residual signs in four-cycle groups give p = 6747/65536 = 0.10295. This approximate test does not reject proportional curves at 0.05. Two cycle harmonics, separate band weights, a narrower orbital window, and all orbital phases give p below 0.05. These controls show that the threshold decision depends on the fit and sample. The soft first-harmonic phase is earlier by 0.005997 cycle, with a conditional descriptive 95% interval that excludes zero. That component result does not imply rejection by the full shape test or a photon travel delay. The tests condition on one selected BAT clock and an assumed residual dependence model. They do not establish equivalent bands or a unique physical cause. We preserve the frozen data, scan selection, projection proof, code, figures, numerical checks, and a full reproduction record.

SMC X-1 · MAXI · Swift BAT · X-ray binaries · superorbital modulation · paired energy bands · weighted projection · residual signs · public astronomical data · reproducible research